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In geometry, a point reflection (also called a point inversion or central inversion) is a transformation of affine space in which every point is reflected across a specific fixed point. When dealing with crystal structures and in the physical sciences the terms inversion symmetry , inversion center or centrosymmetric are more commonly used.
A point reflection is just a type of reflection. In standard reflections, we reflect over a line, like the y-axis or the x-axis. For a point reflection, we actually reflect over a specific point, usually that point is the origin . Formula r(origin) (a, b) → (−a, −b) Formula r ( o r i g i n) ( a, b) → ( − a, − b) Example 1.
Home. Transformations. Reflections. Reflect a Point. Across x axis, y axis and other lines. A reflection is a kind of transformation. Conceptually, a reflection is basically a 'flip' of a shape over the line of reflection. Reflections are opposite isometries, something we will look below. Reflections are Isometries. Reflections are isometries .
A point and its reflection over the line x=-1 have two properties: their y-coordinates are equal, and the average of their x-coordinates is -1 (so the sum of their x-coordinates is -1*2=-2). So (2,3) reflected over the line x=-1 gives (-2-2,3) = (-4,3).
- 4 min
- Sal Khan
- help, what does he mean when the A axis and the b axis is x axis and y axis?They are the same thing: Basically, you can change the variable, but it will still be the x and y-axis.
- How would you reflect a point over the line y=-x?It works just like any line, graph it and follow the line reflection rules. :)
- what if you were reflecting over a line like y = 3When you reflect over y = 0, you take the distance from the line to the point you're reflecting and place another point that same distance from y =...
- (2,-3) is reflected over the y-axis. what is the new coordinates of the point after its reflection?When a point is reflected along the y axis, the X coordinate becomes the opposite number and the y coordinate stays the same. Likewise, when a poin...
Reflections create mirror images of points, keeping the same distance from the line. When we reflect across the y-axis, the image point is the same height, but has the opposite position from left to right.
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- What does prime mean when for example they say C prime?In the context of geometric transformations, the prime symbol (') denotes the image of a point as a result of a transformation. For example, point...
- not as bad as rotating...rotation confuses me90° clockwise rotation: (x,y) becomes (y,-x) 90° counterclockwise rotation: (x,y) becomes (-y,x) 180° clockwise and counterclockwise rotation: (x,...
- how do you identify the reflection of -2,6 ?Depends what axis you are reflecting over, if you are reflecting over x axis, change the y positive or negative sign to the opposite sign, if it re...
- here is another reflecting video: https://www.khanacademy.org/math/basic-geo/basic-geo-transformatio...Thanks! there's actually a way to do it algebraically too, if you don't know it already you'll need it: Across the x-axis -(x,y)- (x,-y) Across the...
- can i get a little bit of explanation?Some basic rules: - Reflection over x-axis: (x, y) ---> (x, -y) - Reflection over y-axis (x, y) ---> (-x, y) - Reflection over line where y = x (x,...
- are you exposed to be in high school ? if so I'm in elementary schoolYou don't have to be in a specific grade to learn the concepts. This is done on purpose so students can learn at their own pace. With that said, do...
- Is reflecting the same thing as rotating 180 degrees about point "x" for example?That depends on the shape. In the case of a square, for example, you could rotate it 90 degrees about the center and get the same thing. However, i...
In geometry, a point reflection (also called a point inversion or central inversion) is a transformation of affine space in which every point is reflected across a specific fixed point. When dealing with crystal structures and in the physical sciences the terms inversion symmetry, inversion center or centrosymmetric are more commonly used.
A reflection is a type of transformation that takes each point in a figure and reflects it over a line. This reflection maps A B C onto the blue triangle over the gold line of reflection. 1 2 3 4 5 6 7 8 9 − 2 − 3 − 4 − 5 − 6 − 7 − 8 − 9 1 2 3 4 5 6 7 8 9 − 2 − 3 − 4 − 5 − 6 − 7 − 8 − 9 y x A B C. The result is a new figure, called the image.
